Results 71 to 80 of about 65,125 (273)
Iterated Function Systems in Mixed Euclidean and p-adic Spaces
, 2006 We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained.
Sing, Bernd
core +2 more sources
Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, EarlyView.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
wiley +1 more source
On fractal faithfulness and fine fractal properties of random variables with independent -digits
Modern Stochastics: Theory and Applications, 2016 We develop a new technique to prove the faithfulness of the Hausdorff–Besicovitch dimension calculation of the family $\varPhi ({Q}^{\ast })$ of cylinders generated by ${Q}^{\ast }$-expansion of real numbers.
Muslem Ibragim, Grygoriy Torbin
doaj +1 more source
ChemSusChem, Volume 18, Issue 6, March 15, 2025.The product profile of enzymatically hydrolyzed PET can be modified by medium engineering and thereby adapted to a desired product. TPA, MHET or BHET can be forced as the predominant product using a basic pH (blue), 25 % ethylene glycol (EG) and IsPETasewt (green) or ≥25 % EG and LCCICCG (pink), respectively.
Tobias Heinks +8 more
wiley +1 more source
Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions
Fractal and FractionalThe Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is ...
Yue Qiu, Yongshun Liang
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Levy processes: Capacity and Hausdorff dimension
, 2005 We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process $X$ in $\mathbf{R}^d$, and a new class of energy forms and their corresponding capacities. We then apply these
Khoshnevisan, Davar, Xiao, Yimin
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Exploring a Novel Conv‐Transformer Network for Multi‐Modality Heart Segmentation
iRADIOLOGY, EarlyView.We propose SFAM‐TransUnet for multimodality whole heart segmentation, a novel deep learning framework combining CNNs and transformers. Extensive experiments conducted on the clinical Multi‐Modality Whole Heart Segmentation datasets demonstrate that SFAM‐TransUnet outperforms various alternative methods.
Youyou Ding +6 more
wiley +1 more source
On estimationes of generalized Hausdorff dimension [PDF]
Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019 This study presents the definition of an abstract homogeneous dimensional space with a finite compactness index, the definition of the Hausdorff–Besicovitch dimension spectrum of such a space, a theorem on the Hausdorff–Besicovitch spectrum values for its subspaces, and a number of results related to these concepts.
A. A. Florinskii, Gennady A. Leonov
openaire +2 more sources
Fractal properties of particle paths due to generalised uncertainty relations
European Physical Journal C: Particles and Fields, 2022 We determine the Hausdorff dimension of a particle path, $$D_\textrm{H}$$ D H , in the recently proposed ‘smeared space’ model of quantum geometry. The model introduces additional degrees of freedom to describe the quantum state of the background and ...
Matthew J. Lake
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On the Dimension of Paracompact Hausdorff Spaces [PDF]
Nagoya Mathematical Journal, 1955 This short note gives the generalized sum theorem for Lebesgue dimension of paracompact Hausdorff spaces. Our theorem, though it is a generalization of Mr. Morita’s sum theorem for fully normal spaces [3, Theorem 3. 2] which is essentially based on his generalized sum theorem for normal spaces [3, Theorem 3.1], is obtained by very brief arguments ...
openaire +3 more sources